Question

Metals A and B crystallize in "simple cubic" and "face centered cubic" lattice respectively. The number of metal atoms A and B per unit cell are respectively:

• A. 2, 4
• B. 1, 4
• C. 2, 1
• D. 1, 2

Hint:

Simple Cubic = 1; Body Centered = 2; Face Centered = 4.

Answer 1

The Correct Option is B

Step 1: Know how atoms are shared.
In a unit cell, an atom at a corner is shared by 8 cells, an atom on a face is shared by 2 cells, and an atom at the body centre belongs fully to one cell.

Step 2: Count the simple cubic cell (metal A).
A simple cubic cell has atoms only at its 8 corners. Each corner gives $1/8$ of an atom, so \[ 8 \times \frac{1}{8} = 1 \text{ atom}. \]

Step 3: Set up the face centred cell (metal B).
A face centred cubic cell has atoms at the 8 corners and at the centre of each of the 6 faces.

Step 4: Count the corner contribution.
The 8 corners give $8 \times \dfrac{1}{8} = 1$ atom.

Step 5: Count the face contribution and total.
The 6 face centres give $6 \times \dfrac{1}{2} = 3$ atoms. Adding, \[ 1 + 3 = 4 \text{ atoms}. \]

Step 6: State the answer.
So A (simple cubic) has 1 atom and B (face centred cubic) has 4 atoms per unit cell.
\[ \boxed{1, 4} \]